Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
arXiv:1103.1014 · doi:10.1088/1742-6596/346/1/012016
Abstract
We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that whenever the low-energy theory in D=3 exhibits an arithmetic "U-duality" symmetry G(Z) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function can be realized as a holomorphic section on the twistor space Z over M. We also offer some comments on the close relation with N=2 wall crossing formulae.
25 pages, contribution to the proceedings of the workshop "Algebra, Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 2010
References in corpus (22)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Wall-Crossing from Boltzmann Black Hole Halos
- Automorphic properties of low energy string amplitudes in various dimensions
- Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
- Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
- Holographic Action for the Self-Dual Field
- D-instantons and twistors
- couplings and automorphic unipotent representations
- On the partition sum of the NS five-brane
- The M5-Brane Elliptic Genus: Modularity and BPS States
- Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
- Quantum mirror symmetry and twistors
- Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
- Large D-instanton effects in string theory
- Duality Groups, Automorphic Forms and Higher Derivative Corrections
- Aspects of higher curvature terms and U-duality
- On the topology of the hypermultiplet moduli space in type II/CY string vacua
- U-Duality and the Compactified Gauss-Bonnet Term
- Geometric quantization and the metric dependence of the self-dual field theory
- A Note on Topological M5-branes and String-Fivebrane Duality
- Wall-crossing of D4-branes using flow trees
- Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons